Onset of $\eta$-meson binding in the He isotopes

Abstract

The onset of binding $\eta$(548) mesons in nuclei is studied in the He isotopes by doing precise $\eta NNN$ and $\eta NNNN$ few-body stochastic variational method calculations for two semi-realistic $NN$ potentials and two energy dependent $\eta N$ potentials derived from coupled-channel models of the $N^{\ast }(1535)$ nucleon resonance. The energy dependence of the $\eta N$ subthreshold input is treated self consistently. It is found that a minimal value of the real part of the $\eta N$ scattering length $a_{\eta N}$ close to 1 fm is required to bind $\eta$ mesons in ${}^3$He, yielding then a few MeV $\eta$ binding in ${}^4$He. The onset of $\eta$-meson binding in ${}^4$He requires that Re$a_{\eta N}$ exceeds 0.7 fm approximately. These results compare well with results of recent $\eta NNN$ and $\eta NNNN$ pionless effective field theory calculations. Related optical-model calculations are also discussed.

arXiv commentv3 -- 18 pages, 6 figures, 4 tables, and matching the published version

References in corpus (22)

• SU(3) Chiral Dynamics with Coupled Channels: Eta and Kaon Photoproduction
• Evolution of Nuclear Spectra with Nuclear Forces
• Chiral Dynamics and the $S_{11}(1535)$ Nucleon Resonance
• Chiral unitary approach to S-wave meson baryon scattering in the strangeness S=0 sector
• Effective Kbar N interaction based on chiral SU(3) dynamics
• Variational calculation of the ppK^- system based on chiral SU(3) dynamics
• $K^{-}pp$ system with chiral SU(3) effective interaction
• Realistic calculations of Kbar-N-N, Kbar-N-N-N, and Kbar-Kbar-N-N quasibound states
• $\eta$ bound states in nuclei
• eta-Nucleon Scattering Length and Effective Range uncertainties
• Eta-nuclear bound states revisited
• Medium effects to N(1535) resonance and eta mesic nuclei
• Pion photoproduction off the proton in a gauge-invariant chiral unitary framework
• Dependence of calculated binding energies and widths of $\eta$-mesic nuclei on treatment of subthreshold $\eta$-nucleon interaction
• Search for eta-mesic 4He in the dd->3He n pi0 and dd->3He p pi- reactions with the WASA-at-COSY facility
• In-medium Eta-Nucleon interactions and Eta nuclear bound states
• Determination of the ${\mathbf{\eta }}^3\mathrm{He}$ threshold structure from the low energy $\mathbf{pd}\to {\mathbf{\eta }}^3\mathrm{He}$ reaction
• Production of $\eta$ and ${\eta }^{\prime }$ Mesons on Nucleons and Nuclei
• Few-body calculations of $\eta$-nuclear quasibound states
• Chirally motivated separable potential model for $\eta N$ amplitudes
• In-medium antikaon and eta-meson interactions and bound states
• The legacy of the experimental hadron physics programme at COSY

Cited by in corpus (14)

• Nuclear effective field theory: status and perspectives
• Etaprime and Eta Mesons with Connection to Anomalous Glue
• Three-Body Hypernuclei in Pionless Effective Field Theory
• Constraining the optical potential in the search for eta-mesic 4He
• $\eta$-nucleus interaction from the $d+d$ reaction around the $\eta$ production threshold
• Search for the $\eta$ mesic ${}^3$He in the $pd\to dp{\pi }^0$ reaction with the WASA-at-COSY facility
• Search for eta mesic 3He with the WASA-at-COSY facility in the pd-> 3He 2gamma and pd-> 3He 6gamma reactions
• Luminosity determination for the proton-deuteron reaction using pd -> 3He eta channel with WASA-at-COSY detector
• Systematic few-body analysis of eta-d, eta-3He and eta-4He interaction at low energies
• Status of the search for $\eta$-mesic nuclei with particular focus on $\eta$-Helium bound states
• On the width of the $K^{-}$D atom ground state
• Probing the existence of η^3He mesic nucleus with a few-body approach
• Onset of $\eta$ nuclear binding
• Dynamically generated hadronic states in the $\bar{K}N$ and $\eta N$ coupled-channels interactions